Joachim Schaefer

State resolved rotational excitation in D2+H2 collisions

In a crossed molecular beam experiment time‐of‐flight distributions of ortho D2 molecules scattered from normal H2 (nH2) and para H2 (pH2) have been measured in a center‐of‐mass angular range of 75° to 180°. The collision energies were 84.1 and 87.2 meV, respectively. In all spectra the rotational excitation of D2 from j=0 to j=2 has been resolved. With pH2 as secondary beam the same transition could also be observed for H2. The measurements show that the probability for rotational excitation of D2 depends on whether the scattering partner H2 is rotating (nH2) or not (pH2). In the first case the cross sections are larger by a factor of approximately 2. The reason for this behavior is the presence of an additional interaction term which is at long range distances, identical to the quadrupole–quadrupole interaction and which is absent if H2 is in the j=0 state. The experimentally derived differential cross sections for the rotational excitation of D2 and H2 are compared with theoretical results obtained by ...

Theoretical studies of H2–H2 collisions. I. Elastic scattering of ground state para‐ and ortho‐H2 in the rigid rotor approximation

Close coupling calculations of integral and differential elastic cross sections of hydrogen ground state molecule collisions have been performed, for c.m. energies below 0.5 eV. It is shown that the isotropic part of the potential, determined by the consistent ab initio potentials of five geometries, provides a very accurate (1%–2%) agreement with measured p‐H2/p‐H2 integral cross sections in the range of 900–2300 m/sec relative velocity. Detailed analysis of p‐H2/p‐H2 scattering results and the determination of a series of orbiting resonances provide a set of (virtual) quasi‐bound‐state energy levels. The fit formula of those levels gives two bound states of the (H2)2 system, for J=0 and 1, at −0.340×10−3 and −0.179×10−3 eV, respectively, which is close to the two binding energies found for the isotropic potential. However, the more attractive plane T configuration of the (H2)2 system gives larger binding energies when the zero point vibrations are neglected. Lifetimes and the periods of orbiting have be...

Theoretical studies of H2–H2 collisions. II. Scattering and transport cross sections of hydrogen at low energies: Tests of a new abinitio vibrotor potential

Close‐coupled calculations of scattering amplitudes have been carried out for H2–H2 collisions for a new ab initio potential energy surface, treating the hydrogen molecules as true vibrotors. The amplitudes were inserted into the kinetic theory expressions for integral and transport cross sections and used to compute (1) the elastic scattering of (j=0, v=0) para‐hydrogen for relative velocities between 1000 and 2500 m/sec; (2) the viscosity differences of ortho‐ and para‐hydrogen for temperatures less than 25 °K; and (3) the thermal diffusion ratio of ortho‐ and para‐hydrogen for temperatures between 50 and 150 °K. The agreement with experiment is highly satisfactory and provides a thoroughgoing test of the new potential energy surface.

Far‐infrared spectra of hydrogen dimers: Comparisons of experiment and theory for (H2)2 and (D2)2 at 20 K

Far‐infrared spectra of weakly bound complexes of molecular hydrogen have been studied using an infrared Fourier transform spectrometer and a long absorption path (98 m) through equilibrium gas at low temperature. The dimer transitions accompany pure rotational transitions of H2 or D2 monomers. Para‐H2 was studied in the S0(0) region (350 cm−1 ), normal H2 in the S0(1) region (590 cm−1 ), and ortho‐D2 in the S0(0) region (180 cm−1 ). The extensive and well resolved (13 sharp lines) spectrum observed for (D2)2 was of special interest. A new empirical (rigid rotor) fit potential of the H2–H2 system has been used for calculating eigenvalues and numerical eigenfunctions of the dimers in the close coupled formalism. Dipole moment transition probabilities were calculated by using the previously tested induced dipole moment surface of Meyer. In order to compare with experiment, bound–bound transition frequencies have been calculated for the three cases, along with the full collision‐induced spectrum for the para...

Quantum studies of inelastic collisions of O2(X 3Σ−g) with He: Polarization effects and collisional propensity rules

We investigate rotationally inelastic cross sections of O2(X 3Σ−g) with He at a collision energy of 27 meV. Theoretical cross sections obtained from close‐coupled (CC) calculations are compared with results from the infinite‐order sudden (IOS) approximation. Both the CC and IOS fine‐structure state‐resolved cross sections exhibit a strong ΔN=ΔJ Fi conserving collisional propensity. An analysis of the general expression for state‐resolved cross sections in terms of spin‐independent tensor opacities clearly establishes, without the introduction of dynamical approximations, the direct connection between this propensity rule and the collisional propensity for the conservation of the orientation of the nuclear rotational angular momentum vector N. In the low‐N limit, Fi changing O2–He collisions are much more strongly depolarizing than collisions that conserve the Fi symmetry level. This enhanced collisional depolarization of an initial distribution of the total molecular angular momentum vector J is related t...

Theoretical studies of H2–H2 collisions. IV. Ab initio calculations of anisotropic transport phenomena in para‐hydrogen gasa)

The temperature dependence of the effective Waldmann–Snider cross sections determining the Senftleben–Beenakker effects of viscosity and heat conductivity has been studied for pH2 gas between 10 and 200 K. From ab initio nonspherical potentials of H2–H2, scattering matrices have been determined in close‐coupling calculations. From these, the elements of the scattering amplitude matrix have been obtained and used as input quantities for the evaluation of the various Waldmann–Snider collision integrals. The results of these first ab initio numerical calculations of anisotropic transport coefficients show excellent agreement of calculated and measured effective cross sections, especially for the most recent improved version of the interaction potential. In addition, it has been shown that the polarization production cross sections are quite sensitive to the potential anisotropy.

Theoretical studies of H2–H2 collisions. V. Ab initio calculations of relaxation phenomena in parahydrogen gas

The temperature dependence of effective Waldmann–Snider cross sections determining relaxation and line broadening phenomena has been studied for p‐H2 between 20 and 200 K. In particular, the rotational relaxation cross section and the relaxation cross sections of the rotational angular momentum vector and tensor polarizations and their respective fluxes have been calculated in an entirely ab initio treatment and close coupling formalism. As far as experimental results were available, quantitative agreement has been obtained. The rotational relaxation cross section has been proven to be quite sensitive to the potential anisotropy. Furthermore, the validity of some approximate relations between effective cross sections has been tested.

The equation of state of hydrogen from an ab initio potential surface

An accurate ab initio calculation of the H2−H2 potential surface has been used to calculate the thermodynamic properties of hydrogen over the temperature range 0–3000 K and at pressures up to 1 Mbar. A comparison with experimental data, including pVT measurements, second virial coefficients and ground state energy, suggests that the surface is significantly in error in the region of the potential minimum. The surface has been scaled semi-empirically to give predictions in acceptable agreement with experimental data. A detailed study of the high density calculations indicated that effects due to the non-sphericity of the potential surface are small.

Line shape cross sections of HD immersed in HE and H2 gas. I. Pressure broadening cross sections

The R(0) and R(1) line shapes of HD are of interest because observation of these lines in the atmosphere of the outer planets should lead to unambiguous values of the D/H ratio. The electronic potential energy surfaces used to calculate HD–He and HD–H2 line shape cross sections have been well validated in previous publications of this series. The results of two additional tests of the electronic potential energy surface of hydrogen‐like systems are reported here: the second virial coefficient of para‐hydrogen at low temperatures and HD–D2 elastic and inelastic differential scattering cross sections. Formulas are given for Dicke narrowing as well as for the line broadening and shift cross sections calculated here. Close coupling calculations were carried out for the R(0) and R(1) transitions of HD immersed in He and for the R(0) transition of HD immersed in H2. These cross sections are anticipated to be quite reliable at temperatures above 50 K, i.e., where clustering can be ignored.

Dimer Features of H2 — H2 and Isotopomers at Low Temperatures

The very successful interaction potential of H2 — H2 determined in ab initio calculations by Meyer and Liu has been empirically improved in the attractive range in order to achieve quantitative agreement with measured second virial coefficients of para-H2 in the temperature range from 16 to 200 K and with measured hyperfme transition frequencies of ortho-H2 — para-H2 and (ortho-H2)2 dimers. We show briefly how this has been done. The resulting rigid- rotor potential has been used to calculate bound state and quasi-bound state dimer eigenvalues and eigen-functions and scattering wave functions of H2 — H2, HD — H2 , and HD — HD in the close coupled approximation to be used in subsequent calculations of absorption spectra. The second block of input data used for this was the ab initio induced dipole moment of H2 — H2 provided and successfully tested by Meyer and colleagues. The dimer features presented in this talk have all been obtained under the assumption of thermal equilibrium. Recent successes and a few points of disagreement found in comparisons of dimer H2 features obtained from the new potential fit and the measurements of McKellar will be briefly mentioned. New results of H2 dimer features in the FIR are shown, including two resonance lines at 1.70 and 1.45 cm-1. The interaction potentials and the induced dipole moments of HD — H2 and HD — HD have been obtained by transforming from the H2 — H2 system, and two examples of isotopomers are shown: 1) Loss and spread of intensity of the R0(0) line of HD strongly diluted in H2 at low temperature (10 and 20 K) is due to the density loss of HD molecules which are bound in HD — H2 dimers. The main contributor to this effect is the permanent dipole moment. 2) The line spectra of the HD — H2 and HD dimers close to the S0(0) frequency of HD (at 20 K) are entirely due to the induced dipole moment.